How to solve geometry word problems that involve geometric figures and angles described in words? You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

Example:

A rectangle is 4 times as long as it is wide. If the length is increased by 4 inches and the width is decreased by 1 inch, the area will be 60 square inches. What were the dimensions of the original rectangle?

Solution:

Step 1: Assign variables:

Let *x* = original width of rectangle

Sketch the figure

Step 2: Write out the formula for area of rectangle.

A = *lw*

Step 3: Plug in the values from the question and from the sketch.

60 = (4*x* + 4)(*x* –1)

Use distributive property to remove brackets

60 = 4*x*^{2} – 4*x* + 4*x* – 4

Put in Quadratic Form

4*x*^{2} – 4 – 60 = 0

4*x*^{2} – 64 = 0

This quadratic can be rewritten as a difference of two squares

(2*x*)^{2} – (8)^{2} = 0

Factorize difference of two squares

(2*x*)^{2} – (8)^{2} = 0

(2*x* – 8)(2*x* + 8) = 0

We get two values for *x*.

2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4

2x + 8 = 0 ⇒ 2x = -8 ⇒ x = -4

Since *x* is a dimension, it would be positive. So, we take *x* = 4

The question requires the dimensions of the original rectangle.

The width of the original rectangle is 4.

The length is 4 times the width = 4 × 4 = 16

Answer: The dimensions of the original rectangle are 4 and 16.

**Writing quadratic equations to solve word problems: Area of a triangle**

Example:

The height of a triangles is 3 cm more than its base. The area of the triangle is 17 cm^{2}. Find the base to nearest hundredth of a cm.

**Find the Dimensions of a Rectangle Word Problem**

Example:

The length of a rectangle is 5 units more than twice its width. If the area is 250 sq. units. then find the dimensions of the rectangle.

**Solve Area World Problems by Factoring**

Example:

A garden that is 4 meters wide and 6 meters long is to have a uniform border such that the area of the border is the same as the area of the garden. Find the width of the border?

**Example of geometry word problem that involves area**

Example:

A rectangle is twice as long as it is wide. If the area of the rectangle is 98 cm^{2}, find its dimensions.

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